GATE EE 2020 Set 1 — Question 45
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Control Systems → Stability Analysis → Feedback & Transfer Function
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Question
Which of the following options is correct for the system shown below?

Correct answer
(C) 4^(th) order and unstable
Solution
The forward path transfer function is .
The feedback path transfer function is .
The characteristic equation is :
The system is of order.
Using the Routh-Hurwitz stability criterion:
There are two sign changes in the first column (20 to -21 and -21 to 20), indicating that the system is unstable. Thus, it is order and unstable.
The feedback path transfer function is .
The characteristic equation is :
The system is of order.
Using the Routh-Hurwitz stability criterion:
There are two sign changes in the first column (20 to -21 and -21 to 20), indicating that the system is unstable. Thus, it is order and unstable.
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